1,834 research outputs found
Extension of the Finite Integration Technique including dynamic mesh refinement and its application to self-consistent beam dynamics simulations
An extension of the framework of the Finite Integration Technique (FIT)
including dynamic and adaptive mesh refinement is presented. After recalling
the standard formulation of the FIT, the proposed mesh adaptation procedure is
described. Besides the linear interpolation approach, a novel interpolation
technique based on specialized spline functions for approximating the discrete
electromagnetic field solution during mesh adaptation is introduced. The
standard FIT on a fixed mesh and the new adaptive approach are applied to a
simulation test case with known analytical solution. The numerical accuracy of
the two methods are shown to be comparable. The dynamic mesh approach is,
however, much more efficient. This is also demonstrated for the full scale
modeling of the complete RF gun at the Photo Injector Test Facility DESY
Zeuthen (PITZ) on a single computer. Results of a detailed design study
addressing the effects of individual components of the gun onto the beam
emittance using a fully self-consistent approach are presented.Comment: 33 pages, 14 figures, 4 table
Gravitational collisions and the quark-gluon plasma
This thesis addresses the thermalisation of heavy-ion collisions within the
context of the AdS/CFT duality. The first part clarifies the numerical set-up
and studies the relaxation of far-from-equilibrium modes in homogeneous
systems. Less trivially we then study colliding shock waves and uncover a
transparent regime where the strongly coupled shocks initially pass right
through each other. Furthermore, in this regime the later plasma relaxation is
insensitive to the longitudinal profile of the shock, implying in particular a
universal rapidity shape at strong coupling and high collision energies.
Lastly, we study radial expansion in a boost-invariant set-up, allowing us to
find good agreement with head-on collisions performed at the LHC accelerator.
As a secondary goal of this thesis, a special effort is made to clearly
expose numerical computations by providing commented Mathematica notebooks for
most calculations presented. Furthermore, we provide interpolating functions of
the geometries computed, which can be of use in other projects.Comment: PhD thesis, 100 pages, 80 figures.
http://dspace.library.uu.nl/handle/1874/294809 , Mathematica notebooks can be
found at sites.google.com/site/wilkevanderschee/phd-thesi
An adaptive grid refinement strategy for the simulation of negative streamers
The evolution of negative streamers during electric breakdown of a
non-attaching gas can be described by a two-fluid model for electrons and
positive ions. It consists of continuity equations for the charged particles
including drift, diffusion and reaction in the local electric field, coupled to
the Poisson equation for the electric potential. The model generates field
enhancement and steep propagating ionization fronts at the tip of growing
ionized filaments. An adaptive grid refinement method for the simulation of
these structures is presented. It uses finite volume spatial discretizations
and explicit time stepping, which allows the decoupling of the grids for the
continuity equations from those for the Poisson equation. Standard refinement
methods in which the refinement criterion is based on local error monitors fail
due to the pulled character of the streamer front that propagates into a
linearly unstable state. We present a refinement method which deals with all
these features. Tests on one-dimensional streamer fronts as well as on
three-dimensional streamers with cylindrical symmetry (hence effectively 2D for
numerical purposes) are carried out successfully. Results on fine grids are
presented, they show that such an adaptive grid method is needed to capture the
streamer characteristics well. This refinement strategy enables us to
adequately compute negative streamers in pure gases in the parameter regime
where a physical instability appears: branching streamers.Comment: 46 pages, 19 figures, to appear in J. Comp. Phy
Computational Electromagnetism and Acoustics
It is a moot point to stress the significance of accurate and fast numerical methods for the simulation of electromagnetic fields and sound propagation for modern technology. This has triggered a surge of research in mathematical modeling and numerical analysis aimed to devise and improve methods for computational electromagnetism and acoustics. Numerical techniques for solving the initial boundary value problems underlying both computational electromagnetics and acoustics comprise a wide array of different approaches ranging from integral equation methods to finite differences. Their development faces a few typical challenges: highly oscillatory solutions, control of numerical dispersion, infinite computational domains, ill-conditioned discrete operators, lack of strong ellipticity, hysteresis phenomena, to name only a few. Profound mathematical analysis is indispensable for tackling these issues. Many outstanding contributions at this Oberwolfach conference on Computational Electromagnetism and Acoustics strikingly confirmed the immense recent progress made in the field. To name only a few highlights: there have been breakthroughs in the application and understanding of phase modulation and extraction approaches for the discretization of boundary integral equations at high frequencies. Much has been achieved in the development and analysis of discontinuous Galerkin methods. New insight have been gained into the construction and relationships of absorbing boundary conditions also for periodic media. Considerable progress has been made in the design of stable and space-time adaptive discretization techniques for wave propagation. New ideas have emerged for the fast and robust iterative solution for discrete quasi-static electromagnetic boundary value problems
Spatially hybrid computations for streamer discharges: II. Fully 3D simulations
We recently have presented first physical predictions of a spatially hybrid
model that follows the evolution of a negative streamer discharge in full three
spatial dimensions; our spatially hybrid model couples a particle model in the
high field region ahead of the streamer with a fluid model in the streamer
interior where electron densities are high and fields are low. Therefore the
model is computationally efficient, while it also follows the dynamics of
single electrons including their possible run-away. Here we describe the
technical details of our computations, and present the next step in a
systematic development of the simulation code. First, new sets of transport
coefficients and reaction rates are obtained from particle swarm simulations in
air, nitrogen, oxygen and argon. These coefficients are implemented in an
extended fluid model to make the fluid approximation as consistent as possible
with the particle model, and to avoid discontinuities at the interface between
fluid and particle regions. Then two splitting methods are introduced and
compared for the location and motion of the fluid-particle-interface in three
spatial dimensions. Finally, we present first results of the 3D spatially
hybrid model for a negative streamer in air
FDTD modelling of electromagnetic transformation based devices
PhDDuring this PhD study, several finite-difference time-domain (FDTD) methods were
developed to numerically investigate coordinate transformation based metamaterial
devices. A novel radially-dependent dispersive FDTD algorithm was proposed and
applied to simulate electromagnetic cloaking structures. The proposed method can ac-
curately model both lossless and lossy cloaks with ideal or reduced parameters. It was
demonstrated that perfect “invisibility” from electromagnetic cloaks is only available
for lossless metamaterials and within an extremely narrow frequency band. With a
few modifications the method is able to simulate general media, such as concentrators
and rotation coatings, which are produced by means of coordinate transformations
techniques. The limitations of all these devices were thoroughly studied and explo-
red. Finally, more useful cloaking structures were proposed, which can operate over a
broad frequency spectrum.
Several ways to control and manipulate the loss in the electromagnetic cloak ba-
sed on transformation electromagnetics were examined. It was found that, by utili-
sing inherent electric and magnetic losses of metamaterials, as well as additional lossy
materials, perfect wave absorption can be achieved. These new devices demonstrate
super-absorptivity over a moderate wideband range, suitable both for microwave and
optical applications.
Furthermore, a parallel three-dimensional dispersive FDTD method was introdu-
ced to model a plasmonic nanolens. The device has its potential in subwavelength
imaging at optical frequencies. The finiteness of such a nano-device and its impact
on the system dynamic behaviour was numerically exploited. Lastly, a parallel FDTD
method was also used to model another interesting coordinate transformation based
device, an optical black hole, which can be characterised as an omnidirectional broad-
band absorber
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